The global refugee population experiencing international displacement has alarmingly doubled in the past decade, now exceeding 37.6 million individuals. These massive movements often leave refugees in critical conditions, with limited access to essential resources and services. Humanitarian organizations play a vital role in mitigating these challenges through targeted relief aid interventions. However, the strategic optimization of these efforts has received limited attention in academic research. This study addresses the Dynamic Mobile Facility Location Problem with Uncertain Mobile Demand (DMFLP-UMD), focusing on cost-efficient strategies for meeting the recurring needs of dispersed refugee groups traveling toward safe destinations. The problem involves deploying capacitated mobile facilities to deliver relief aid periodically and equitably in terms of service frequency. The DMFLP-UMD is modeled as a Markov Decision Process (MDP) with decision-dependent probabilistic state transitions informed by key migration drivers. To solve the problem, we propose an Approximate Policy Iteration (API) algorithm, enhanced with custom basis functions that account for critical factors such as refugee populations, distances to destination points, and migration velocities. The algorithm uses a Least Squares Temporal Differences (LSTD) learning framework to estimate policy vectors effectively. Additionally, we introduce a state-dependent variable threshold policy, providing decision-makers with a rapid and reliable method to generate high-quality relief plans. The methodologies are validated through case studies based on the recent Syria-Türkiye migration crisis. The results highlight significant operational advantages, showcasing how these approaches can improve resource allocation and service delivery. The study offers actionable insights for managing current and future refugee crises.

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